Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
Solution
The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.
Correct Answer: A — 2
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Q. What is the sum of the roots of the equation 2x^2 - 3x + 1 = 0?
Solution
The sum of the roots is given by -b/a = 3/2.
Correct Answer: B — 3/2
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Q. What is the sum of the roots of the equation 2x^2 - 4x + 1 = 0?
Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer: B — 1
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Q. What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?
Solution
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Correct Answer: B — 4
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Q. What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?
Solution
The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the equation x^2 - 4x + 3 = 0?
Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
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Q. What is the sum of the roots of the quadratic equation f(x) = x^2 - 5x + 6?
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation x^2 - 4x + 3 = 0?
Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
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Q. What is the sum of the roots of the quadratic equation x^2 - 5x + 6 = 0?
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation x^2 - 7x + 10 = 0?
Solution
The sum of the roots is given by -b/a = 7/1 = 7.
Correct Answer: C — 7
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Q. What is the term containing x^2 in the expansion of (3x + 4)^4?
-
A.
144
-
B.
216
-
C.
432
-
D.
576
Solution
The term containing x^2 is given by C(4,2) * (3x)^2 * 4^2 = 6 * 9 * 16 = 864.
Correct Answer: B — 216
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Q. What is the term independent of x in the expansion of (3x - 4)^7?
Solution
The term independent of x occurs when k = 7, C(7, 3) * (3)^3 * (-4)^4 = 35 * 27 * 256 = 84.
Correct Answer: C — 84
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Q. What is the total number of subsets of the empty set?
Solution
The empty set has exactly one subset, which is itself: ∅.
Correct Answer: B — 1
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Q. What is the total number of subsets of the set G = {1, 2, 3, 4, 5}?
Solution
The total number of subsets is 2^5 = 32.
Correct Answer: A — 32
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Q. What is the total number of terms in the expansion of (x + 2y)^6?
Solution
The total number of terms is n + 1 = 6 + 1 = 7.
Correct Answer: C — 8
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Q. What is the trace of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Solution
The trace of A is the sum of the diagonal elements: 1 + 5 + 9 = 15.
Correct Answer: A — 15
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Q. What is the union of the sets I = {1, 2} and J = {2, 3}?
-
A.
{1, 2, 3}
-
B.
{1, 2}
-
C.
{2, 3}
-
D.
{1, 2, 2, 3}
Solution
The union of two sets includes all unique elements from both sets. Thus, I ∪ J = {1, 2, 3}.
Correct Answer: A — {1, 2, 3}
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Q. What is the union of the sets {1, 2} and {2, 3}?
-
A.
{1, 2}
-
B.
{1, 2, 3}
-
C.
{2, 3}
-
D.
{1, 2, 2, 3}
Solution
The union of two sets includes all elements from both sets without duplicates. Thus, {1, 2} ∪ {2, 3} = {1, 2, 3}.
Correct Answer: B — {1, 2, 3}
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Q. What is the union of the sets {a, b} and {b, c}?
-
A.
{a, b}
-
B.
{a, b, c}
-
C.
{b, c}
-
D.
{a, c}
Solution
The union of two sets is the set of elements that are in either set. Here, {a, b} ∪ {b, c} = {a, b, c}.
Correct Answer: B — {a, b, c}
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Q. What is the unit vector in the direction of (3, 4)?
-
A.
(3/5, 4/5)
-
B.
(4/5, 3/5)
-
C.
(1, 1)
-
D.
(0, 0)
Solution
Unit vector = (3, 4) / √(3^2 + 4^2) = (3/5, 4/5).
Correct Answer: A — (3/5, 4/5)
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Q. What is the unit vector in the direction of (3, 4, 0)?
-
A.
(0.6, 0.8, 0)
-
B.
(0.8, 0.6, 0)
-
C.
(1, 0, 0)
-
D.
(0, 1, 0)
Solution
Unit vector = (3, 4, 0) / √(3^2 + 4^2) = (3, 4, 0) / 5 = (0.6, 0.8, 0).
Correct Answer: A — (0.6, 0.8, 0)
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Q. What is the unit vector in the direction of (4, 3)?
-
A.
(4/5, 3/5)
-
B.
(3/4, 4/3)
-
C.
(1, 1)
-
D.
(0, 1)
Solution
Unit vector = (4/5, 3/5) where magnitude = √(4^2 + 3^2) = 5
Correct Answer: A — (4/5, 3/5)
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Q. What is the unit vector in the direction of the vector (4, 3)?
-
A.
(4/5, 3/5)
-
B.
(3/5, 4/5)
-
C.
(1, 0)
-
D.
(0, 1)
Solution
Unit vector = (4/5, 3/5) since magnitude = 5.
Correct Answer: A — (4/5, 3/5)
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Q. What is the unit vector in the direction of v = (3, 4)?
-
A.
(0.6, 0.8)
-
B.
(1, 1)
-
C.
(3, 4)
-
D.
(0, 0)
Solution
Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)
Correct Answer: A — (0.6, 0.8)
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Q. What is the unit vector in the direction of vector A = (3, 4)?
-
A.
(0.6, 0.8)
-
B.
(0.8, 0.6)
-
C.
(1, 1)
-
D.
(0, 0)
Solution
Unit vector = A / |A| = (3, 4) / 5 = (0.6, 0.8).
Correct Answer: A — (0.6, 0.8)
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Q. What is the value of (1 + i)^2?
-
A.
2i
-
B.
2
-
C.
0
-
D.
1 + 2i
Solution
(1 + i)^2 = 1^2 + 2*1*i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer: A — 2i
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Q. What is the value of (2 + 3)^3 using the binomial theorem?
-
A.
27
-
B.
125
-
C.
216
-
D.
343
Solution
Using the binomial theorem, (2 + 3)^3 = 5^3 = 125.
Correct Answer: A — 27
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Q. What is the value of 2sin(θ)cos(θ)?
-
A.
sin(2θ)
-
B.
cos(2θ)
-
C.
tan(θ)
-
D.
sec(θ)
Solution
By the double angle identity, 2sin(θ)cos(θ) = sin(2θ).
Correct Answer: A — sin(2θ)
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Q. What is the value of cos(0°)?
-
A.
0
-
B.
1
-
C.
-1
-
D.
undefined
Q. What is the value of cos(180°)?
-
A.
0
-
B.
-1
-
C.
1
-
D.
Undefined
Solution
cos(180°) = -1.
Correct Answer: B — -1
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Showing 2611 to 2640 of 2847 (95 Pages)
